Most people would agree that they seem to sound best when singing in the shower. What few people realize is that the physics behind it is the same physics that make most musical instruments sound the way they do. All of this boils down to waves superimposing on each other.

Pure and Impure Tones

A pure tone is a sound wave that is composed of one frequency. Due to this, a pure tone is said to be unchanging. Pure tones are what musical instruments produce.

Impure tones are sounds that are composed of many different frequencies. These tones tend to be interpreted as noise by the human ear.

In physics, impure tones are actually just a combination of many pure tones that are produced at the same time.

The role of these two types of tones will become important later on. For now, the focus shifts to musical instruments.

Musical Instruments and the Superposition of Waves

Musical instruments produce sounds in various ways. However, the sound produced is amplified and given its characteristic twang through two processes, both of which involve the superposition of waves.

For the first method of superposition, let’s take the simplest possible scenario; a tube that is open on one end and closed on the other.

Half-open tube

Fig. 1. The half-open tube, the basis of many musical instruments.

Most musical instruments produce  the sound outside the instrument’s body. Furthermore, any particular sound has a frequency and a wavelength. So at this time, two pure tones of different frequencies will be analysed. These two waves are produced at the same time, but are analysed on separate images for clarity.

Half-open tube with constructive interference

Fig. 2a. Wave A. Note that at this time, there are 2.5 wavelengths in the tube. The wave’s displacement is at the maximum at the opening, and zero at the closed end.

Half-open tube with destructive interference

Fig. 2b. Wave B. The wave’s displacement is at the maximum at the opening, but is not zero at the closed end.

When the sound wave hits the closed end of the tube, it gets reflected. The result is that the sound wave undergoes superposition, and the wave interferes with itself. What exactly happens depends on the wavelength and the length of the tube.

Half-open tube with constructive interference reflected

Fig. 3a. For wave A, the wave forms a stationary wave pattern.

Half-open tube with destructive interference reflected

Fig. 3b. Wave B is reflected, but does not form the pattern of a stationary wave.

When the sound waves are superimposed to form a stationary wave, not much happens in terms of its wavelength, and so the frequency also does not change. The same could not be said about the interference that do not make stationary waves. Instead, the following happens.

Half-open tube with destructive interference reflected 2

Fig. 4. Wave B produces the longer-wavelength pattern as it undergoes superposition on itself the 1st time. The sound source then places more of the sound wave into the tube, which can be seen as a copy of the original wave (shorter wavelength).

The destructive interference would keep on happening until the wave cancels itself out. When it does, the amplitude of the wave becomes zero. For sound, this means that is is either very soft, or no sound comes out at all.

What does this have to do with showers?

The human voice is not a pure tone. Instead, it is a combination of many tones. The combination of tones produced gives each of us our distinctive voices.

Human Voice Wave Form

Fig. 5. This is how the human voice wave form looks like. Not really a pure tone, is it?

Most bathrooms are small, with solid walls, and very few things that absorb sound. This allows it to behave like the open tube described above.

Bathroom

Fig. 6. A bathroom, also known as a sound chamber.

When a person sings in the shower, the impure tone that is the human voice bounces off the walls of the bathroom. the different pure tones of different wavelengths of the voice separate. Those pure tones that have the right wavelengths make stationary waves when reflected. The others get cancelled out. The end result: pure tones of the right relationships to each other. In other words, the correct musical notes.

So the next time you sing in the shower, you may want to calculate the right wavelengths produced. Or better yet, simply enjoy the shower knowing physics can explain how you sound better in the bathroom. Happy singing!